Partial correlation for a linear transform of independent normals

Suppose $\begin{pmatrix}X_1\\X_2\\X_3\end{pmatrix}\sim N_3\!\left(\begin{pmatrix}0\\0\\0\end{pmatrix},\begin{pmatrix}1&0&0\\0&1&0\\0&0&1\end{pmatrix}\right)$ and $\begin{pmatrix}X\\Y\\mathbb{Z}\end{pmatrix}=\begin{pmatrix}3&0&0\\2&2&0\\4&0&4\end{pmatrix}\begin{pmatrix}X_1\\X_2\\X_3\end{pmatrix}$. Then the partial correlation coefficient $\rho_{YZ\cdot X}$ is